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If its EXACTLY on the beam, then see above. The trouble is tidal current is very rarely exactly on the beam and a little different either f'wd or aft makes a big difference to the answer as to what you are actually doing 'through the water'. It's one of the reasons we like to have a log as well as a GPS...

If, according to the GPS I am making 6 knots SOG but have a 3 knot cross tide on my beam, how much of the 6 knots is forward speed as against sideways slip due to the tide?

If everything remained constant you would indeed travel six miles in one hour but of course that won't happen

If the cross tide is genuinely at 90 degrees to your track then you will actually have a speed thru the water in excess of 6 knots. If the cross tide is say 30 degrees forward of your track then you will actually being doing in the region of 7.5 knots thru the water, if the cross tide is 30 degrees aft of your track then you will only be doing about 4.5 knots thru the water!

Now where the fun really starts is if you perceive the cross tide to be on the beam but in practice it is forward or aft by 60 degrees...........in this case your boat speed thru the water may be as high as 9 knots or as low as 3 knots..........you see where I'm coming from!!